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We develop a consistent adaptive framework in a multilevel collocated grid layout for simulating two-phase flows with adaptive mesh refinement (AMR). The conservative mo-mentum equations and the mass equation are solved in the present consistent framework. This consistent mass and momentum transport treatment greatly improves the accuracy and robustness for simulating two-phase flows with a high density ratio and high Reynolds number. The interface capturing level set method is coupled with the conservative form of the Navier–Stokes equations, and the multilevel reinitialization technique is applied for mass conservation. This adaptive framework allows us to advance all variables level by level using either the subcycling or the non-subcycling method to decouple the data ad-vancement on each level. The accuracy and robustness of the framework are validated by a variety of canonical two-phase flow problems. We demonstrate that the consistent scheme results in a numerically stable solution in flows with high density ratios(up to 106) and high Reynolds numbers(up to 106), while the inconsistent scheme exhibits non-physical fluid behaviors in these tests. Furthermore, it is shown that the subcycling and non-subcycling methods provide consistent results and that both of them can accurately resolve the interfaces of the two-phase flows with surface tension effects. Finally, a 3D breaking wave problem is simulated to show the efficiency and significant speedup of the proposed framework using AMR. 

We develop a consistent adaptive framework in a multilevel collocated grid layout for simulating two-phase flows with adaptive mesh refinement (AMR). The conservative mo-mentum equations and the mass equation are solved in the present consistent framework. This consistent mass and momentum transport treatment greatly improves the accuracy and robustness for simulating two-phase flows with a high density ratio and high Reynolds number. The interface capturing level set method is coupled with the conservative form of the Navier–Stokes equations, and the multilevel reinitialization technique is applied for mass conservation. This adaptive framework allows us to advance all variables level by level using either the subcycling or the non-subcycling method to decouple the data ad-vancement on each level. The accuracy and robustness of the framework are validated by a variety of canonical two-phase flow problems. We demonstrate that the consistent scheme results in a numerically stable solution in flows with high density ratios(up to 106) and high Reynolds numbers(up to 106), while the inconsistent scheme exhibits non-physical fluid behaviors in these tests. Furthermore, it is shown that the subcycling and non-subcycling methods provide consistent results and that both of them can accurately resolve the interfaces of the two-phase flows with surface tension effects. Finally, a 3D breaking wave problem is simulated to show the efficiency and significant speedup of the proposed framework using AMR. 

Despite the cariogenic role of Candida suggested from recent studies, oral Candida acquisition in children at high risk for early childhood caries (ECC) and its association with cariogenic bacteria Streptococcus mutans remain unclear. Although ECC disproportionately afflicts socioeconomically disadvantaged and racial-minority children, microbiological studies focusing on the underserved group are scarce. Our prospective cohort study examined the oral colonization of Candida and S. mutans among 101 infants exclusively from a low-income and racial-minority background in the first year of life. The Cox hazard proportional model was fitted to assess factors associated with the time to event of the emergence of oral Candida and S. mutans. Oral Candida colonization started as early as 1 wk among 13% of infants, increased to 40% by 2 mo, escalated to 48% by 6 mo, and remained the same level until 12 mo. S. mutans in saliva was detected among 20% infants by 12 mo. The emergence of S. mutans by year 1 was 3.5 times higher (hazard ratio [HR], 3.5; confidence interval [CI], 1.1–11.3) in infants who had early colonization of oral Candida compared to those who were free of oral Candida ( P = 0.04) and 3 times higher (HR, 3.0; CI, 1.3–6.9) among infants whose mother had more than 3 decayed teeth ( P = 0.01), even after adjusting demographics, feeding, mother’s education, and employment status. Infants’ salivary S. mutans abundance was positively correlated with infants’ Candida albicans ( P < 0.01) and Candida krusei levels ( P < 0.05). Infants’ oral colonization of C. albicans was positively associated with mother’s oral C. albicans carriage and education ( P < 0.01) but negatively associated with mother’s employment status ( P = 0.01). Future studies are warranted to examine whether oral Candida modulates the oral bacterial community as a whole to become cariogenic during the onset and progression of ECC, which could lead to developing novel ECC predictive and preventive strategies from a fungal perspective. 

We consider the isoperimetric problem for the sum of two Gaussian densities in the line and the plane. We prove that the double Gaussian isoperimetric regions in the line are rays and that if the double Gaussian isoperimetric regions in the plane are half-spaces, then they must be bounded by vertical lines.